sztuczne sieci neuronowe w analizie efektywnoœci skrawania

sztuczne sieci neuronowe w analizie efektywnoœci skrawania

Dariusz MAZURKIEWICZ
SZTUCZNE SIECI NEURONOWE W ANALIZIE
EFEKTYWNOŒCI SKRAWANIA MATERIA£ÓW
KRUCHYCH UK£ADAMI WIELOOSTRZOWYMI
ARTIFICIAL NEURAL NETWORKS IN EFFICIENCY
ANALYSIS OF BRITTLE MATERIALS CUTTING
PROCESS WITH MULTI-PICK HEADS
W artykule przedstawiono wyniki analizy danych laboratoryjnych uzyskanych w trakcie procesu skrawania materia³ów kruchych g³owicami wieloostrzowymi z wykorzystaniem sztucznych
sieci neuronowych. Analiza dotyczy problemu efektywnoœci procesu skrawania w zale¿noœci od
geometrii wieloostrzowego uk³adu skrawaj¹cego. Celem pracy by³o miêdzy innymi przetestowanie mo¿liwoœci zastosowania sieci neuronowych w rozwi¹zywaniu problemów analizy procesu skrawania.
S³owa kluczowe: skrawanie, materia³y kruche, g³owice wieloostrzowe, sieci neuronowe
In the paper there are presented some analysis results of laboratory data recorded during natural
brittle materials cutting process with the use of multi-pick cutting heads. Artificial neural networks
were used as an analysis tool. The aim of the analysis was to get new information about cutting
process efficiency depending on cutting tools set geometry, but also to test the possibility of
neural networks applications in solving of cutting process problems.
Keywords: cutting process, brittle materials, multi-pick heads, neural networks
1. Introduction
Typical real-world problems usually have quantitative and qualitative dimensions. In such a case, especially for decision making we need to process both –
quantitative and qualitative information. The same
happens when we analyze any technological process,
for example such as cutting of natural brittle materials with the use of multi-pick heads. All systems and
processes are identified by their measurable components. If we can measure all necessary components
(parameters) of analyzed process or any other system,
and we are also able to formalize relations among these
parameters by mathematical functions, then we can
use quantitative methods to analyze the system (process), solve all problems and make necessary predictions or recommend decisions [12].
Artificial neural networks (ANN) and expert systems provide the needed methodologies, which deal
with qualitative aspects of decision-making and processes parameters predictions. In our case – to make
efficiency analysis of brittle materials cutting process
with multi-pick heads, we tried to test performance of
different architectures of artificial neural networks. All
this, because unfortunately, it is still very common that
personal experience is used to determine cutting values because the complexity of machining process and
its conditions very often cannot be described with reliable calculation methods. In addition many engineering and especially geological problems are characterized by being very complex, uncertain and
undefined, due to for example lack of data or knowledge. On the other hand - some results presented in
references show, that these problems can be successfully solved with support of artificial neural networks
and other intelligent systems [2, 9, 10].
Results obtained during researches with the use of
artificial neural networks are presented in this paper.
We have taken into consideration typical geometrical
parameters of the multi-pick cutting heads having influence on the cutting process efficiency, there is cutting depth (hD), angular scale between cutters (t0) and
their lateral scale (t). These parameters, their influence on the cutting process together with laboratory experiments, during which real-world data used in ANN
teaching, training and verification were described in
several previous papers [4, 5, 6, 7, 8].
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2. ANN in cutting data analysis and predictions
ting forces values Fc1, Fc2 and Fc3 were measured on
three Rapid 83 tools of the multi-pick set, as a function
of their geometrical parameters – there is their positioning on the cutting head described by cutting depth (hD),
angular scale (t0) and lateral scale (t).
It means that these three geometrical parameters
were input variables, and three cutting force values –
output variables of the network. For this purpose we
have tested several different architectures to choose
one with the best performance. In each case we had
95 training sets, 47 verification sets and 47 test sets of
the experimental data. Also for each case we have
compared such networks as:
• linear
• Radial Basis Function (RBF)
• generalized regression neural networks (GRNN)
• radial basis function networks (RBF)
• multi-layer perceptrons (MLP)
• and probabilistic neural networks (PNN).
For each of them we have analyzed network sensivity, error, performance (regression ratio) and correlation. The best results were obtained when GRNN
and RBF networks were used (fig. 1, fig. 2, fig. 3, fig.
4). The GRNN network has quite complex architecture with 95 neurons in the first hidden layer, while
another one is simple, having single hidden layer only
with six neurons.
For both architectures taken into further analysis
and comparison we have calculated regression statistics, which results are presented in table 1 (GRNN 395-4-3) and table 2 (RBF 3-6-3), where for each data
set we display:
• Data Mean – average value for the target variable
At present time artificial neural networks, as on of
Data Mining tool are successfully used to solve sophisticated technological problems [1, 2, 3, 9, 10]. This
way, unknown relations between input and output
parameters can be learned and reproduced by neural
networks. Such representation obtained when modeling technological objects with the use of ANN can
be qualitative. It means that no mathematical function is needed to represent these relations. All this
happens inside the ANN as a kind of relations and
interconnections between neurons and layers, depending of used architecture.
Fig. 1. Network with one of the best performances
(GRNN 3-95-4-3)
In our case we wanted to make a kind of intelligent
determination of cutting forces values with the help of
artificial neural network. We wanted to make some predictions of cutting forces values on three tools set as a
function of multi-pick heads geometrical parameters.
To train, verify and test the networks we have used data
sets obtained during laboratory experiments, when cut3
2,8
2,6
2,4
2,2
2
1,8
1,6
1,4
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47
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39
37
35
33
31
29
27
25
23
21
19
17
15
13
9
11
7
5
3
1
1
1,2
Fig. 2. Real values of cutting forces on the first tool of the set (continuous line) and their predictions (dot line) GRNN 3-95-4-3 network, test set of the experimental data
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• Data S. D. – standard deviation of the target output
variable
• Error Mean – average error (residual between target
and actual output values) of the output variable,
• Abs. E. Mean – average absolute error (difference
between target and actual output values) of the output variable
• Error S. D. – standard deviation of errors of the
output variable
• S. D. Ratio – the error: data standard deviation ratio
• Correlation – the standard Pearson-R correlation
coefficient between the target and actual values
General regression neural networks (GRNN) perform regression rather than classification tasks. The
GRNN networks copy the training cases into the network to be used to estimate response of new points.
The output is estimated using weighted average of the
outputs of training cases, where the weighting is related to the distance of the point from the point being
estimated. The best GRNN network with the best performance in our investigation consisted of four layers.
Input layer of 3 units (three input variables), two hidden layers with 95 neurons in the first one and 4 units
in the second one), and finally – output layer with three
neurons because of three output variables taken into
consideration. The first hidden contains radial units,
second one – contains units which help to estimate
weighted average. This is a specialized procedure [11].
Each output has a special unit assigned in this layer
which forms the weighted sum for the corresponding
output. To get the weighted average from the weighted
sum, the weighted sum must be divided through by the
sum of weighting factors. A single special unit in the
second layer calculates the latter value. The output layer then performs the actual division [11]. Hence, the
Fig. 3. Network with one of the best performances
(RBF 3-6-3)
second hidden layer always has exactly one more unit
than the output layer (in our case 4 units in the second
hidden layer and three in output layer). The training
process and architecture of the GRNN 3-95-4-3 network
shows that they train almost instantly, but usually are
large and slow. This disadvantage is quite clear when
we compare the GRNN 3-95-4-3 and RBF 3-6-3 networks. Obtained results represented by the network
performance is almost equal, while architecture’s complexity is completely different – the first one is quite
complex (95 units in the first hidden layer), while the
second one consists only of 6 neurons in a single hidden layer.
Radial basis function network, which has obtained
the best performance (RBF 3-6-3) have an input layer
of three neurons (because we had 3 input, there is independent variables), one hidden layer of radial units
and output layer of linear units. The network has three
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2,6
2,4
2,2
2
1,8
1,6
1,4
1,2
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9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49
Fig. 4. Real values of cutting forces on the first tool of the set (continuous line) and their predictions (dot line) - RBF
3-6-3 network, test set of the experimental data
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Table 1 -Regression statistics for GRNN 3-95-4-3
Training Verification Test Training Verification Test Training Verification Test
Fc1
Fc1
Fc1
Fc2
Fc2
Fc2
Fc3
Fc3
Fc3
2.4578
2.4108 2.3061
2.3325
2.6595 2.4077
2.3606
2.3300
Data Mean 2.4583
0.3550
0.3232
0.4379 0.3692
0.3695
2.6895 0.3454
0.3222
0.3758
Data S.D.
0.0048
0.0045
0.0201 0.0058
0.0674
0.3983 0.0067
0.0157
0.0301
Error
Mean
0.2088
0.2833 0.1614
0.2522
2.6968 0.1596
0.1854
0.2138
Error S.D. 0.2007
0.1482
0.1674
0.1928 0.1229
0.1849
0.5618 0.1196
0.1397
0.1706
Abs. E.
Mean
0.6460
0.6470 0.4373
0.5825
0.1027 0.4621
0.5752
0.5690
S.D. Ratio 0.5652
0.7654
0.8097 0.9160
0.7315
08242 0.9045
0.8204
0.8342
Correlation 0.8401
Table 2 -Regression statistics for RBF 3-6-3
Training Verification Test Training Verification Test Training Verification Test
Fc1
Fc1
Fc1
Fc2
Fc2
Fc2
Fc3
Fc3
Fc3
2.4206
2.4868 2.2785
2.3365
2.7112 2.3788
2.3614
2.3876
Data Mean 2.4391
0.3479
0.3734
0.4077 0.3699
0.3998
2.6779 0.3596
0.3082
0.3656
Data S.D.
0.0001
0.0216
0.0596 0.0001
0.038
0.4328 0.0001
0.0274
0.0139
Error
Mean
0.2187
0.2957 0.2120
0.2509
2.6984 0.2090
0.1860
0.2270
Error S.D. 0.1832
0.1421
0.1779
0.1912 0.1591
0.2005
0.5605 0.1667
0.1529
0.1885
Abs. E.
Mean
0.5856
0.7253 0.5730
0.6276
0.3663 0.5813
0.6035
0.6210
S.D. Ratio 0.5267
0.8147
0.6896 0.8149
0.7793
0.7899 0.8136
0.8020
0.7839
Correlation 0.8501
output neurons, because the object has three dependent variables – cutting forces values on three tools of
the set. The radial layer has exponential activation
functions, the output layer – linear activation functions (the activation level is passed on directly as the
output). RBF network was trained in three stages:
- the centers stored in the radial hidden layer were
optimized first, typically using unsupervised training techniques, for which we have used different algorithms, like: K-means, Kohonen training
or learned vector quantization, to place centers
to reflect clustering,
- the spread of data was reflected in the radial deviations (stored in the threshold), deviations can
be typically assigned by a number of algorithms
(explict, isotropic, K-nearest neighbor),
- the linear output layer was optimized using pseudo-inverse technique, as this is fast and guarantees to minimize the error if deviations are too small.
It was noticed that the RBF network was trained
relatively quickly and did not extrapolate too far from
known data. From references describing theory of artificial neural networks, we know that a perfect prediction will have correlation coefficient of 1. On the
other hand such correlation does not necessarily indicate a perfect prediction (only a prediction which is
perfectly linearly correlated with the actual outputs),
although in practice the correlation coefficient is
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a good indicator of performance [11]. It also provides
a simple way to compare the performance of networks
with standard least squares linear fitting procedures.
In our researches for the GRNN and RBF networks
the correlation was usually equal to 0.8, and was a little bit higher for the first one. Comparing obtained
performance and our knowledge about analyzed object, which very often can be influenced by random
factors and several disturbances can be considered as
high and satisfactory.
3. Final conclusions
Determination of cutting forces values on multipick heads cutting natural brittle materials with the
help of artificial neural networks is a new, alternative
and promising method. Results from our several tests, when we have been using different architectures,
training methods, activation functions, etc., typical for
neural networks theory show, that networks are capable of learning different functions from experimental
databases, including those nonlinear.
Our laboratory experiments which aim was efficiency analysis of brittle materials cutting process with the
use of multi-pick cutting heads were complicated and
limited. But they helped us to get a dataset with information about cutting heads geometrical parameters influence cutting forces measured on three tools of the
set. This information and knowledge coming from its
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analysis provided further possibility for problem description when modeling the object with the use of Finite Element Method [5, 6]. It was one of the possibilities to extend investigations and get new knowledge
about the object. On the other hand – artificial neural
networks which application possibility for cutting pro-
cess analysis was presented in this paper can be successfully used as an alternative tool. They can be used
not only for dependent variables predictions beyond
laboratory test limitations, but also for interpretation,
diagnosis and further real-time control, monitoring or
optimization of the cutting process.
References
[1] Ikeda Y., Mazurkiewicz D., 2000 - "Data Mining Aided Analysis In Laser Diagnostic Experiments". Discovery
Science 2000, Progress Report Edited by S. Arikawa, M. Sato, T. Sato, A. Marouka, S. Miyano, Y. Kanada.
Kyoto (Japan), December 2000, pp.: 88-90.
[2] Lipski J., 2001 - "Identyfikacja procesów dynamicznych z zastosowaniem sieci neuronowch". Maintenance
and Reliability, kwartalnik PN-TTE i PAN O/Lublin - Journal of the Polish Academy of Sciences and the
Polish Maintenance Society. Nr. 5, 2001, pp.:. 15-17.
[3] Mazurkiewicz D., 1999 - "Data Mining - new concept in data processing". Maintenance and Reliability,
kwartalnik PN-TTE i PAN O/Lublin - Journal of the Polish Academy of Sciences and the Polish Maintenance
Society. Nr 2/1999, pp.: 24-30
[4] Mazurkiewicz D., 2000 - "Computer Aided Modeling and Simulations in Rock Cutting Process Analysis".
Eksploatacja i NiezawodnoϾ - Maintenance and Reliability, kwartalnik PN-TTE i PAN O/Lublin - Journal of
the Polish Academy of Sciences and the Polish Maintenance Society. Nr. 6, 2000, pp.:. 27-40
[5] Mazurkiewicz D., 2000 - "Empiricieskije i analiticieskije modeli processa riezanija gornych porod". FizikoTehnicieskie Problemy Razrabotki Poleznyh Iskopajemyh, Rossijskaja Akademija Nauk, (Journal of the Soviet
Academy of Science published in Russian language), No. 5/2000, pp.: 75-81.
[6] Mazurkiewicz D., 2000 - "Empirical and analytical models of cutting process of rocks". Journal of Mining
Science by Kluwer Academic/Plenum Publishers, Vol. 36, No. 5. 2000, pp.: 481-486.
[7] Mazurkiewicz D., 2001 - "Wp³yw wybranych parametrów konstrukcyjnych uk³adów wieloostrzowych na
efektywnoœæ skrawania materia³ów skalnych". Eksploatacja i Niezawodnoœæ - Maintenance and Reliability,
kwartalnik PN-TTE i PAN O/Lublin - Journal of the Polish Academy of Sciences and the Polish Maintenance
Society. Nr. 4, 2001 , pp.: 31-37.
[8] Mazurkiewicz D., 2001- "Analiza procesu skrawania materia³ów kruchych pochodzenia naturalnego
z wykorzystaniem Metody Elementów Skoñczonych". Eksploatacja i Niezawodnoœæ - Maintenance and Reliability,
kwartalnik PN-TTE i PAN O/Lublin - Journal of the Polish Academy of Sciences and the Polish Maintenance
Society. Nr. 5, 2001 , pp.: 72-74.
[9] Nestler A., Schulz G., 1999 - "Cutting values prediction with neural networks". 0
[10] Prostañski D., Jonak J., 2001 - "Problemy wykorzystania sieci neuronowej do identyfikacji procesu skrawania
ska³". Maintenance and Reliability, kwartalnik PN-TTE i PAN O/Lublin - Journal of the Polish Academy of
Sciences and the Polish Maintenance Society. Nr. 5/2001, pp.:18-20.
[11] Reference Manual of SNN software.
[12] Zahedi F., 1999 - "Intelligent systems for business: expert systems with neural networks". Wadsworth Publishing
Company, Belmond 1999.
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Artyku³ prezentuje wyniki prac otrzymanych w ramach realizacji projektu badawczego
KBN PB-1505/T12/99/16
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Dr in¿. Dariusz Mazurkiewicz
Katedra Podstaw In¿ynierii Produkcji
Politechnika Lubelska
ul. Nadbystrzycka 36
20-618 Lublin
e-mail: [email protected]
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